From Longman Dictionary of Contemporary Englishdry coughdry coughMIa cough which does not produce any phlegm → dry
Examples from the Corpus
dry cough• Copious, thick, ropy mucus from the larynx; hoarseness, rough voice, dry cough.• I was already coughing a dry cough.• Thick, yellow, offensive ear discharges with loss of hearing and dry cough.• Usually loose but sometimes can be a dry cough.• A short dry cough, may be a little watery mucus, possibly blood streaked.• Hard, dry cough racks the whole chest. 